An iterative algorithm for solving the multidimensional neutron diffusion nodal method equations on parallel computers

Journal Article · Fri May 01 04:00:00 EDT 1992 · Nuclear Science and Engineering; (United States)

OSTI ID:5204366

Kirk, B L; Azmy, Y Y ^[1]

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1. Oak Ridge National Lab., Oak Ridge, TN (US)

In this paper the one-group, steady-state neutron diffusion equation in two-dimensional Cartesian geometry is solved using the nodal integral method. The discrete variable equations comprise loosely coupled sets of equations representing the nodal balance of neutrons, as well as neutron current continuity along rows or columns of computational cells. An iterative algorithm that is more suitable for solving large problems concurrently is derived based on the decomposition of the spatial domain and is accelerated using successive overrelaxation. This algorithm is very well suited for parallel computers, especially since the spatial domain decomposition occurs naturally, so that the number of iterations required for convergence does not depend on the number of processors participating in the calculation. Implementation of the authors' algorithm on the Intel iPSC/2 hypercube and Sequent Balance 8000 parallel computer is presented, and measured speedup and efficiency for test problems are reported. The results suggest that the efficiency of the hypercube quickly deteriorates when many processors are used, while the Sequent Balance retains very high efficiency for a comparable number of participating processors. This leads to the conjecture that message-passing parallel computers are not as well suited for this algorithm as shared-memory machines.

• DOE Contract Number: AC05-84OR21400
• OSTI ID: 5204366
• Journal Information: Nuclear Science and Engineering; (United States), Journal Name: Nuclear Science and Engineering; (United States) Vol. 111:1; ISSN 0029-5639; ISSN NSENA
• Country of Publication: United States
• Language: English

Related Subjects

663610* -- Neutron Physics-- (1992-)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
CARTESIAN COORDINATES
COMPUTERS
COORDINATES
DIFFERENTIAL EQUATIONS
EFFICIENCY
EQUATIONS
INTEGRALS
ITERATIVE METHODS
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL LOGIC
NEUTRON DIFFUSION EQUATION
PARALLEL PROCESSING
PROGRAMMING
TESTING
TWO-DIMENSIONAL CALCULATIONS